Render an object from "all" perspectives
You can use the Curves Extra Objects Add-on to create a spiral and convert this into a Path. A Follow Path constraint and Track To constraint on your camera will then allow your camera to follow the spiral whilst tracking the object. 

While it isn't strickly each 'face' (since it's a spiral rather than a set of concentric circles) it might suit your particular requirement or be able to be "adjusted" to suit - eg, by adding drivers to 'modulo' the coordinates to force them to be in discrete steps rather than continuous.

To achieve this, first go to File/User Preferences... and select Add-ons. Find the 'Add Curve: Extra Objects' and enable it.

You should now have a Spirals option in the Add/Curve menu in the 3d View.

Add a Spiral, set Spiral Type to '3' and set Turns and Steps to the desired values.



Select the spiral and select Object/Convert To/Curve from Mesh to convert it to a curve.

Move the camera to 0,0,0 and add Follow Path and Track To constraints as shown :



This can produce the following result :